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A classification of special Riemannian 3-manifolds with distinct constant Ricci eigenvalues. (English) Zbl 0821.53036
This paper is a contribution to the explicit description of the metrics of a three-dimensional curvature homogeneous Riemannian space, that is, a Riemannian manifold with constant Ricci eigenvalues $$\rho_ i$$, $$i = 1,2,3$$. The case of equal eigenvalues is well known and the case $$\rho_ 1 = \rho_ 2 \neq \rho_ 3$$ has been treated in detail by the first author. Here, the authors treat the case of distinct eigenvalues and obtain an explicit description under two additional geometrical assumptions by solving explicitly an associated system of first-order partial differential equations.

MSC:
 53C20 Global Riemannian geometry, including pinching 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C30 Differential geometry of homogeneous manifolds
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References:
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